Kevin Rudd and Julie Bishop in 2011. Ms Bishop says the government will consider supporting Mr Rudd's bid to become UN Secretary-General if he nominates. Photo: Alex Ellinghausen

"Should Kevin Rudd nominate then of course the Australian government would consider what sort of support he would require," she said in New York.

While the role is expected to go to an Eastern European candidate when Mr Ban leaves office at the end of the year, Mr Rudd is an outside chance and is understood to have been lobbying hard for the role, despite his public denials.

Former New Zealand prime minister Helen Clark, who is the administrator of the United Nations Development Programme, is also in contention.

Mr Rudd and Ms Bishop were once direct parliamentary adversaries, when he was foreign minister and she his shadow, sharing some fiery public exchanges. But behind the scenes they were friendly. Ms Bishop's support would be considered critical to his chances.